Two-dimensional arrays of holes with sub-lithographic diameters formed by block copolymer self-assembly

ABSTRACT

Methods for fabricating sublithographic, nanoscale microstructures in two-dimensional square and rectangular arrays utilizing self-assembling block copolymers, and films and devices formed from these methods are provided.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a division of U.S. patent application Ser. No. 11/657,273, filed Jan. 24, 2007, now U.S. Pat. No. 8,394,483, issued Mar. 12, 2013.

TECHNICAL FIELD

Embodiments of the invention relate to methods of fabricating nanostructures by use of thin films of self-assembling block copolymers, and devices resulting from those methods.

BACKGROUND OF THE INVENTION

As the development of nanoscale mechanical, electrical, chemical and biological devices and systems increases, new processes and materials are needed to fabricate nanoscale devices and components. Optical lithographic processing methods are not able to accommodate fabrication of structures and features at the nanometer level. The use of self-assembling diblock copolymers presents another route to patterning at nanometer dimensions. Diblock copolymer films spontaneously assembly into periodic structures by microphase separation of the constituent polymer blocks after annealing, for example by thermal annealing above the glass transition temperature of the polymer or by solvent annealing, forming ordered domains at nanometer-scale dimensions. Following self assembly, one block of the copolymer can be selectively removed and the remaining patterned film used as an etch mask for patterning nanosized features into the underlying substrate. Since the domain sizes and periods (L_(o)) involved in this method are determined by the chain length of a block copolymer (MW), resolution can exceed other techniques such as conventional photolithography, while the cost of the technique is far less than electron beam (E-beam) lithography or EUV photolithography, which have comparable resolution.

The film morphology, including the size and shape of the microphase-separated domains, can be controlled by the molecular weight and volume fraction of the AB blocks of a diblock copolymer to produce lamellar, cylindrical, or spherical morphologies, among others. For example, for volume fractions at ratios greater than about 80:20 of the two blocks (AB) of a diblock polymer, a block copolymer film will microphase separate and self-assemble into a periodic spherical domains with spheres of polymer B surrounded by a matrix of polymer A. For ratios of the two blocks between about 60:40 and 80:20, the diblock copolymer assembles into a periodic hexagonal close-packed or honeycomb array of cylinders of polymer B within a matrix of polymer A. For ratios between about 50:50 and 60:40, lamellar domains or alternating stripes of the blocks are formed. Domain size typically ranges from 5-50 nm.

Periodic cylindrical structures have been grown in parallel and perpendicular orientations to substrates. A primary requirement for producing perpendicular cylinders by thermal annealing is that the substrate floor must be neutral wetting to the blocks of the copolymer. Periodic hexagonal close-packed cylinders can be useful as etch masks to make structures in an underlying substrate for applications such as magnetic storage devices. However, that layout is not useful for making structures such as DRAM capacitors, which require a rectangular- or square-shaped array layout.

Graphoepitaxy techniques using substrate topography have been used in an attempt to influence the orientation, ordering and registration of the microphase-separated domains. Although one-dimensional arrays have been formed in trenches, no efforts have been made to address ordering of the domains over a large area, or to control the location and orientation of ordered domains in two dimensions.

Although there is a single report of forming ordered sphere-forming block copolymer films by Cheng et al. (Nano Lett., 6 (9), 2099-2103 (2006)), these have been limited to one-dimensional ordered arrays with adjacent arrays not aligned, the cylinders being off-set along the y-axis in neighboring trenches.

It would be useful to provide methods of fabricating films of two-dimensional arrays of ordered nanostructures that overcome these problems.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention are described below with reference to the following accompanying drawings, which are for illustrative purposes only. Throughout the following views, the reference numerals will be used in the drawings, and the same reference numerals will be used throughout the several views and in the description to indicate same or like parts.

FIGS. 1A-4A illustrate diagrammatic top plan views of a portion of a substrate during various stages of fabrication of a film composed of a two-dimensional rectangular array of perpendicular oriented cylinders in a polymer matrix according to an embodiment of the present disclosure. FIGS. 1B/1C-4B/4C are elevational, cross-sectional views of the substrate fragment depicted in FIGS. 1A-4A, taken along lines 1B/1C-1B/1C to lines 4B/4C-4B/4C, respectively.

FIGS. 5A-11C illustrate various stages of the fabrication of a film composed of a two-dimensional square array of perpendicular oriented cylinders in a polymer matrix according to another embodiment of the present disclosure. FIGS. 5A-5C illustrate elevational, cross-sectional views of a portion of a substrate during stages of producing a material layer. FIG. 6 is a cross-sectional view of the substrate depicted in FIG. 5C in a subsequent step with a self-assembling block copolymer material within trenches. FIGS. 7A-11A are diagrammatic top plan views of a portion of the substrate of FIG. 6, during subsequent stages of the fabrication of a film composed of a two-dimensional square array of cylinders in a polymer matrix. FIGS. 7B-11B are elevational, cross-sectional views of the substrate depicted in FIGS. 7A-11A, taken along lines 7B-7B to lines 11B-11B, respectively. FIG. 11C is a cross-sectional view of the substrate of FIG. 10A in a subsequent processing step showing selective removal of the matrix of the annealed film in another embodiment.

FIGS. 12A-18A illustrate diagrammatic top plan views of a portion of a substrate during various stages of fabrication of a film composed of a two-dimensional rectangular array of perpendicular oriented and parallel oriented cylinders in a polymer matrix according to another embodiment of the present disclosure. FIGS. 12B, 13B and 15B-18B are elevational, cross-sectional views taken along lines B of the substrate depicted in FIGS. 12A, 13A and 15A-18A, respectively. FIG. 14 is an elevational, cross-sectional view of the substrate of FIG. 13A in a subsequent processing step.

DETAILED DESCRIPTION OF THE INVENTION

The following description with reference to the drawings provides illustrative examples of devices and methods according to embodiments of the invention. Such description is for illustrative purposes only and not for purposes of limiting the same.

In the context of the current application, the terms “semiconductor substrate” or “semiconductive substrate” or “semiconductive wafer fragment” or “wafer fragment” or “wafer” will be understood to mean any construction comprising semiconductor material, including but not limited to bulk semiconductive materials such as a semiconductor wafer (either alone or in assemblies comprising other materials thereon), and semiconductive material layers (either alone or in assemblies comprising other materials). The term “substrate” refers to any supporting structure including, but not limited to, the semiconductive substrates, wafer fragments or wafers described above.

“L_(o)” is the inherent pitch (bulk period or repeat unit) of structures that self-assemble upon annealing from a self-assembling (SA) block copolymer or a blend of a block copolymer with one or more of its constituent homopolymers.

In embodiments of the invention, processing conditions are used that induce microphase separation of thin films of self-assembling cylindrical-phase diblock copolymers to produce 2-D rectangular and square arrays of nanoscale cylinders by constraining one dimension by graphoepitaxy and the second dimension either by graphoepitaxy or by chemically differentiating the trench floor.

Steps in a method for fabricating two-dimensional (2-D) rectangular arrays of cylinders oriented perpendicular to a substrate from thin films of cylindrical phase self-assembling (SA) block copolymers according to an embodiment of the invention are illustrated in FIGS. 1A-4C. The described embodiment is a graphoepitaxy-only technique, which utilizes topographical features, the sidewalls and ends of trenches, as constraints to induce orientation and registration of perpendicularly-oriented cylindrical copolymer domains in both one dimension (single row parallel to the trench sidewalls) and a second dimension (cylinders registered between adjacent trenches) to achieve 2-D rectangular arrays of nanoscale microstructures in the form of cylinders within a polymer matrix.

Referring to FIGS. 1A and 1B, a substrate 10 with an overlying material layer 12 is provided, being a silicon layer 10 and a silicon oxide (SiO_(x)) layer 12 in the illustrated example.

To prepare a 2-D rectangular array of cylinders according to a first embodiment of a method of the invention, the material layer 12 is patterned to form an array of adjacently aligned trenches 14 a _(1-3, 14) b ₁₋₃, 14 c ₁₋₃. Each trench is structured with sidewalls 16, a floor or bottom surface 18, a width (w), and a length (l). Substrate 10 is exposed as the floor 18 of the trench, and portions of the material layer 12 form a spacer interval 12 a between the trenches. The width (w) of the trenches is equal to about the inherent pitch value (L_(o)) of the polymer, typically ranging from about 10-100 nm. The length (l) of the trenches is equal to about nL_(o) (“n*L_(o)”), typically ranging from about n*10-n*100 nm (with n being the number of features/structures (i.e., cylinders)). First edges (ends or tips) 20 a and second edges 20 b of each adjacent trench (e.g., trenches 14 a ₁-14 b ₁-14 c ₁) are aligned, as shown in FIG. 1A. As such, each adjacent trench is substantially the same the length (l). In some embodiments, the trench dimension is about 55-80 nm wide (w) and 1600-2400 nm in length (l). The depth (D) of the trenches can range from about 50-500 nm. The spacing or pitch distance (p_(t)) between adjacent trenches can vary but is at least 2L_(o).

The trenches can be formed using a lithographic tool having an exposure system capable of patterning at the scale of L_(o) (10-100 nm). Such exposure systems include, for example, extreme ultraviolet (EUV) lithography, proximity X-rays, and electron beam lithography, as known and used in the art. Conventional photolithography can attain ˜58 nm features.

The trench sidewalls 16 and edges 20 a, 20 b influence the structuring of the array of cylinders within the trenches. The boundary conditions of the trench sidewalls 16 impose order in the x-direction (x-axis) and ends 20 impose order in the y-direction (y-axis) to impose a structure wherein each trench contains n number of features (i.e., cylinders). Factors in forming a single 1-D array of cylinders aligned within the center and for the length of each trench include the width of the trench, the formulation of the block copolymer to achieve the desired pitch (L_(o)), and the thickness (t) of the copolymer film. To achieve a single array (row) of cylinders within each trench, the trench is constructed to have a width (w) of about the L_(o) value of the polymer and a length (l) of nL_(o). The application and annealing of a block copolymer material having an inherent pitch value of L_(o) will result in a single array of “n” cylinders in the middle of a polymer matrix for the length (l) of the trench, with each cylinder being separated by a value of L_(o).

For example, a block copolymer having a 35-nm pitch (L_(o) value) deposited into a 75-nm wide trench will, upon annealing, result in a zigzag pattern of 35-nm diameter cylinders that are offset by a half-distance for the length of the trench, rather than a single line of cylinders down the center of the trench. As the L_(o) value of the copolymer is increased, for example, by forming a ternary blend by the addition of both constituent homopolymers, there is a shift from two rows to one row of cylinders within the center of the trench.

The lithographically-defined alignment of the trench edges 20 a, 20 b imposes a second dimension of ordering such that each one-dimensional (1-D) array of cylinders (i.e., in trench 14 b ₁) will line up with the adjacent 1-D arrays of cylinders (i.e., in trenches 14 a ₁ and 14 c ₁). Stresses due to trench length and/or width mismatch with the inherent pitch of the block copolymer can be relieved by elliptical variance from circularity in the x- or y-axis direction, as described, for example, by Cheng et al. (Nano Lett., 6 (9), 2099-2103 (2006)).

As shown in FIGS. 1A and 1B, an array or string of three adjacent trenches 14 a-c has been etched into material layer 12 (e.g., oxide). The trenches are structured such that the surfaces of the sidewalls 16 and edges 20 a, 20 b are preferential wetting by the minority block of the copolymer and the trench floors 18 are neutral wetting (equal affinity for both blocks of the copolymer) to allow both blocks of the copolymer material to wet the floor 18 of the trench. Entropic forces drive the wetting of a neutral-wetting surface by both blocks, resulting in a perpendicular orientation of the self-assembled morphology.

A neutral wetting surface can be provided, for example, by applying a neutral wetting polymer to form a neutral wetting film 22 on the surface of the substrate 10 forming the trench floors 18, as illustrated in FIGS. 1A and 1B. In the use of a SA diblock copolymer composed of PS-b-PMMA, a random PS:PMMA copolymer brush layer (P(S-r-MMA)), which exhibits non-preferential or neutral wetting toward PS and PMMA can be applied by spin-coating onto the trench floor 18 (i.e., the surface of substrate 10). The brush can be affixed by grafting (on an oxide substrate) or by crosslinking (any surface) using UV radiation. In an embodiment shown in FIG. 1C, a random copolymer solution can be applied to substrate 10′ as a blanket film 22′ before deposition of the material layer 12′. For example, a random copolymer solution composed of PS and PMMA (58% PS) can be applied to the surface of the substrate 10 as a layer about 5-10 nm thick and end-grafted by heating at about 160° C. for about 48 hours. Etching through the material layer 12′ to form the trenches 14′ then exposes the underlying random copolymer film layer 22′ as the floor 18′ of the trench.

A surface that is neutral wetting to PS-b-PMMA can also be prepared by spin coating a photo- or theimally crosslinkable random copolymer such as benzocyclobutene- or azidomethylstyrene-functionalized random copolymers of styrene and methyl methacrylate (e.g., poly(styrene-r-benzocyclobutene-r-methyl methacrylate (P(S-r-PMMA-r-BCB)) onto the surface of the substrate 10 within the trenches and thermally crosslinking the polymer (e.g., 190° C., 4 hours) to form a crosslinked polymer mat. Capillary forces pull the random copolymer to the bottom of deep trenches. Non-crosslinked polymer material can be subsequently removed. In another embodiment, the crosslinkable polymer can be applied as a blanket film 22′ to the substrate 10′ before deposition of the material layer 12′, and exposed upon etching of the trenches 14′, as depicted in FIG. 1C. Another neutral wetting surface for PS-b-PMMA can be provided by hydrogen-terminated silicon, which can be prepared by a conventional process, for example, by a fluoride ion etch of silicon (with native oxide present, about 12-15 Å) (e.g., as substrate 10), for example, by immersion in aqueous solutions of hydrogen fluoride (HF) and buffered HF or ammonium fluoride (NH₄F), HF vapor treatment, etc., by exposure to hot H₂ vapor or by a hydrogen plasma treatment (e.g., atomic hydrogen).

The surface of the sidewalls 16 and the edges 20 a, 20 b of the trenches are preferential wetting by one of the components of the block copolymer to induce formation of the cylinders down the middle of each trench as the blocks self-assemble. For example, silicon oxide (SiO_(x)) exhibits preferential wetting toward the PMMA block to result in the assembly of a thin interface layer of PMMA on the trench sidewalls as well as PMMA cylinders in the center of a PS matrix within each trench. Other preferential wetting surfaces to PMMA can be provided, for example, by silicon nitride, silicon oxycarbide, and PMMA polymer grafted to a sidewall material such as silicon oxide, and resist materials such as such as methacrylate based resists. Upon annealing, the PMMA block of the PS-b-PMMA copolymer layer will segregate to the sidewalls and edges of the trench to form a wetting layer (33 in FIGS. 3A-3C). The material layer 12 itself can be a preferential wetting material (e.g., SiO_(x)), although a layer of a preferential wetting material can be applied onto the surfaces of the trenches. For example, a polymethylmethacrylate (PMMA) that is modified with a moiety containing one or more hydroxyl (—OH) groups (e.g., hydroxyethylmethacrylate) can be applied by spin coating and then heating (e.g., to about 170° C.) to allow the terminal OH groups to end-graft to the oxide sidewalls 16 and edges 20 a, 20 b of the trenches. Non-grafted material can be removed from the neutral wetting layer 22 by rinsing with an appropriate solvent (e.g., toluene). See, for example, Mansky et al., Science 275: 1458-1460 (1997)).

Referring now to FIGS. 2A and 2B, a cylindrical-phase SA block copolymer material 24 having an inherent pitch at or about L_(o) (or a ternary blend of block copolymer and homopolymers blended to have a pitch at or about L_(o)) is then deposited, typically by spin casting (spin-coating), onto the floor 18 of the trenches. The block copolymer material can be deposited onto the patterned surface by spin casting from a dilute solution (e.g., about 0.25-2 wt % solution) of the copolymer in an organic solvent such as dichloroethane (CH₂Cl₂) or toluene, for example.

The copolymer material layer 24 is deposited into the trenches to a thickness (t) of less than or about equal to the L_(o) value of the copolymer material to up to about 3L_(o), such that the copolymer film layer will self-assemble upon annealing to form a single row of perpendicular cylindrical domains having a diameter of about L_(o) (e.g., 25-35 nm) in the middle of a polymer matrix within each trench. The film thickness can be measured, for example, by ellipsometry.

Depending on the depth (D) of the trenches, the cast block copolymer material 24 can fill the trenches as in FIG. 2B where the trench depth is about equal to L_(o) (D˜L₀), or form a thin film 24′ over the trench floor 18′ or optionally over the trench sidewalls 16′ and edges 20 a′, 20 b′ as in FIG. 2C where the trench depth is greater than L_(o) (D>L₀), e.g., a meniscus. The height (h) of the assembled cylinders (FIGS. 3B and 3C) corresponds approximately to the thickness (t) of the deposited copolymer material 24, 24′ within the trench. Although not shown, a thin film of the copolymer material 24 can be deposited onto the surface of the oxide layer 12; this material will not self-assemble, as it is not thick enough to form structures.

Although diblock copolymers are used in the illustrative embodiment, other types of block copolymers (i.e., triblock or triblock or multiblock copolymers) can be used. Examples of diblock copolymers include poly(styrene-block-methyl methacrylate) (PS-b-PMMA), polyethyleneoxide-polyisoprene, polyethyleneoxide-polybutadiene, polyethyleleoxide-polystyrene, polyetheleneoxide-polymethylmethacrylate, polystyrene-polyvinylpyridine, polystyrene-polyisoprene (PS-b-PI), polystyrene-polybutadiene, polybutadiene-polyvinylpyridine, and polyisoprene-polymethylmethacrylate, among others. Examples of triblock copolymers include poly(styrene-block methyl methacrylate-block-ethylene oxide). An examples of a PS-b-PMMA copolymer material (L_(o)=35 nm) is composed of about 70% PS and 30% PMMA with a total molecular weight (M_(n)) of 67 kg/mol, to form ˜20 nm diameter cylindrical PMMA domains in a matrix of PS.

The block copolymer material can also be formulated as a binary or ternary blend comprising a SA block copolymer and one or more homopolymers of the same type of polymers as the polymer blocks in the block copolymer, to produce blends that swell the size of the polymer domains and increase the L_(o) value of the polymer. The volume fraction of the homopolymers can range from 0% to about 40%. An example of a ternary diblock copolymer blend is a PS-b-PMMA/PS/PMMA blend, for example, 46K/21K PS-b-PMMA containing 40% 20K polystyrene and 20K poly(methylmethacrylate). The L_(o) value of the polymer can also be modified by adjusting the molecular weight of the block copolymer.

Optionally, ellipticity (“bulging”) can be induced in the structures by creating a slight mismatch between the trench and the spacer widths and the inherent pitch (L_(o)) of the block copolymer or ternary blend, as described, for example, by Cheng et al., “Self-assembled One-Dimensional Nanostructure Arrays,” Nano Lett., 6 (9), 2099-2103 (2006), which then reduces the stresses that result from such mismatches.

Referring now to FIGS. 3A and 3B, the block copolymer film 24 is then annealed as by theimal annealing above the glass transition temperature of the component blocks of the copolymer material to cause the polymer blocks to separate and self-assemble according to the pattern of wettability on the underlying surfaces of the trenches to form the self-assembled block copolymer structure 28. For example, a PS-b-PMMA copolymer film can be annealed at a temperature of about 180-195° C. in a vacuum oven for about 1-24 hours to achieve the self-assembled morphology. The film can also be solvent annealed, for example, by slowly swelling both blocks of the film with a solvent, then slowly evaporating the solvent.

The annealed copolymer film comprises a rectangular array of perpendicularly oriented cylindrical domains 30 of a first block of the copolymer within a matrix 32 of a second block, the cylindrical domains in one dimension at a pitch distance of about L_(o) and aligned with cylindrical domains in a second dimension at a pitch distance of about 2*L_(o). The annealed copolymer film can be contained within adjacently spaced apart trenches with the ends (edges) 20 a, 20 b of the trenches being aligned, and with the cylindrical domains within each trench in a single array and at a pitch distance of about L_(o) and aligned with the cylindrical domains in adjacent trenches at a pitch distance of about 2*L_(o).

The constraints provided by the width (w) of trenches and the character of the copolymer composition combined with a neutral wetting trench floor 18 and preferential wetting sidewalls 18 and edges 20 a, 20 b, results, upon annealing, in a one-dimensional (1-D) array (single row) of perpendicularly-oriented, cylindrical domains 30 of PMMA within a matrix 32 of PS within each trench 14 a-14 c, with n structures according to the length of the trench, and a thin layer 33 of PMMA wetting the sidewalls 18.

The additional feature of the alignment of the trench edges 20 a, 20 b in combination with a pitch distance (p_(t)) of adjacent trenches substantially equal to 2L_(o), achieves two-dimensional (2-D) rectangular arrays 28 a-28 c of cylindrical domains 30 in which the pattern period or pitch distance (p_(c)) of the cylinders 30 within a single trench (e.g., 14 a ₃) is substantially equal to L_(o) and the pitch distance (p_(c2)) between the cylinders 30 of adjacent trenches (e.g., 14 a ₃ and 14 b ₃) is substantially equal to 2*L_(o) (2L₀) as depicted in FIG. 3A.

The resulting morphologies of the block copolymer (i.e., perpendicular orientation of cylinders) can be examined, for example, using atomic force microscopy (AFM), transmission electron microscopy (TEM), and scanning electron microscopy (SEM).

After annealing and the copolymer material is ordered, one of the block components can be selectively removed from the film, leaving either the cylindrical domains 30 (FIG. 4B) or the matrix 32 (FIG. 4C) resulting in rectangular arrays 28 a-28 c of openings or coverings (structures). After selective removal of one of the polymer domains, the resulting thin films can be used, for example, as a lithographic template or mask to pattern the underlying substrate 10 in a semiconductor processing to define regular patterns in the nanometer size range (i.e., about 10-100 nm).

For example, referring to FIGS. 4A and 4B, selective removal of the PMMA phase cylinders 30 will result in 2-D rectangular arrays of openings 34 within a thin film of polystyrene (PS) within the trenches 14 a-c with the oxide layer 12 a remaining a spacer between each trench. Removal of the PMMA phase cylinders 30 can be performed, for example, by application of an oxygen (O₂) plasma, or by a chemical dissolution process such as acetic acid sonication by first irradiating the sample (ultraviolet (UV) radiation, 1 J/cm^2 254 nm light), then ultrasonicating the film in glacial acetic acid, ultrasonicating in deionized water, and rinsing the film in deionized water to remove the degraded PMMA.

In another embodiment illustrated in FIG. 4C, the selective removal of a PMMA phase matrix 32 will provide 2-D rectangular arrays of PS phase cylinders 30 and openings 34′. Such an embodiment would require a majority PMMA block copolymer and sidewalls composed of a material that is selectively PMMA-wetting (e.g. oxide).

The resulting porous PS film can be used as an etch mask to pattern (arrows ↓↓) the underlying substrate 10, for example, by a non-selective RIE etching process, to form a rectangular array of openings 35 in substrate 10 (shown in phantom in FIGS. 4A and 4B) for the fabrication of devices such as capacitors. Further processing can then be performed as desired.

A method according to another embodiment of the invention utilizing a graphoepitaxy-only technique is illustrated with reference to FIGS. 5A-11C, for forming two-dimensional (2-D) square arrays of perpendicularly-oriented cylinders in a polymer matrix.

In an embodiment to form a 2-D square array, a construction as described with reference to FIGS. 1A-1C can be provided, which includes a substrate 10′ bearing a neutral wetting surface, for example, by application of a neutral wetting material layer 22″, and an overlying material layer 12″ having trenches 14 a ₁₋₃″-14 c ₁₋₃″ formed therein to expose the neutral wetting material layer 22″ as the trench floors 18″. In one embodiment, for example, a neutral wetting material layer 22″ such as an end-grafted neutral wetting random (PS:PMMA) copolymer brush can be formed on the substrate 10″, and then layer 12″ deposited, as described with reference to FIG. 1C. Neutral wetting trench floors 18″ can also be provided as H-terminated silicon, which can be prepared, for example, by a fluoride ion etch of a silicon substrate 10″ (with native oxide present, about 12-15 Å), for example, by immersion in aqueous solutions of hydrogen fluoride (HF) and buffered HF or ammonium fluoride (NH₄F), HF vapor treatment, etc., or by exposure to hot H₂ vapor or by a hydrogen plasma treatment (e.g., atomic hydrogen). As in FIGS. 1A-1C, each trench 14 a ₁₋₃″-14 c ₁₋₃″ is separated by a spacer interval 12 a″ of the material layer 12″ of a width (w_(i)) of about L_(o).

In this embodiment, the sidewalls 16″ of the material layer 12″ are preferential wetting to the major block of the SA block copolymer, being PS in the illustrated example. Preferential wetting surfaces to PS can be provided, for example, by a metal such as gold or a PS-based photoresist containing a photoacid generator. For example, the material layer 12″ itself can be composed of metal (e.g., gold), or the sidewalls 16″ of the material layer 12″ can be coated with a thin film of metal, for example, by evaporation, sputtering, or a spin-on technique, with removal of the metal from the trench floors 18″ (e.g., by etching). For example, a metal (e.g., gold) layer of about 2-10 nm can be applied by thermal evaporation onto surfaces of the trenches formed within a material layer 12″ of oxide, which surface can be precoated with a seed layer (e.g., chromium) as an adhesive interface.

In an embodiment with reference to FIG. 5A, a neutral wetting layer 22″ (e.g., a random copolymer, H-terminated silicon, etc.) is formed on the substrate 10″. Then, as illustrated, a photoresist layer 36″ is applied onto the neutral wetting layer 22″, baked, patterned and developed to form a series of grooves 37″. For example, a random copolymer brush of PS (58% vol.) and PMMA can be grafted onto a silicon substrate to provide a neutral wetting layer 22″, and a PMMA resist 36″ applied (e.g., by spin-coating), baked (about 130° C.) to remove residual solvent, patterned (e.g., by electron beam lithography), and developed by immersing in solvent. As shown in FIG. 5B, a layer of metal can then be deposited to form the material layer 12″. The remaining photoresist 36″ and overlying metal can then be removed. Such a liftoff process results in a structure as in FIG. 5C (and in top plan view in FIG. 1A). For example, a layer of chromium and of gold can be sequentially deposited by evaporation, and the PMMA photoresist and overlying deposited metal removed to result in gold features with grooves between the features. As shown, a series of metal features (e.g., gold) form the material layer 12″ with sidewalls 16″ and spacer intervals 12 a″ between adjacent trenches (e.g., between 14 a ₃″, 14 b ₃″, and 14 c ₃″), and grooves or trenches 14 a ₁₋₃″-14 c ₁₋₃″ with the exposed neutral wetting layer 22″ as the trench floors 18″. Upon annealing a block copolymer film (e.g., of PS-b-PMMA) within the trenches, the major block (e.g., PS) will wet the surface of the sidewalls of the trenches (as shown in FIGS. 7A and 7B).

Referring now to FIG. 6, a cylindrical-phase SA block copolymer material 24″ (as described with reference to FIGS. 2A and 2B) is then deposited into the trenches and annealed. The resulting self-assembled block copolymer structure 28″, illustrated in FIGS. 7A and 7B, is composed of 2-D rectangular arrays 28 a″-28 c″ of cylinders 30″ of the minor block (e.g., PMMA) within a matrix 32″ of the major block (e.g., PS), which also wets the sidewalls 16″ of the trenches.

Following the annealing and ordering of the copolymer material 24″, the polymer film 28″ is crosslinked to fix and enhance the strength of the self-assembled polymer blocks. The polymers may be structured to inherently crosslink (e.g., upon UV exposure), or one or both of the polymer blocks of the copolymer material can be formulated to contain a crosslinking agent, which can be the same crosslinking agent if used in forming the neutral wetting film 22″ on the trench floors 18″ (as in the step of FIGS. 1A-1C).

Referring now to FIGS. 8A and 8B, following the crosslinking of the film 28″, the spacer interval 12 a″ of the material layer 12″ (e.g., gold) situated between adjacent trenches (e.g., between 14 a ₃″, 14 b ₃″, and 14 c ₃″) is then removed, for example, by a selective wet etch with aqua regia, to produce an intermediate structure with new trenches 15 a ₁₋₃″-15 b ₁₋₃″ of width (w_(l)) at or about L_(o). As illustrated, the removal exposes the matrix 32 composed of the major block (e.g., PS) to form the sidewalls 40″ of the trenches 15″, and exposes the neutral wetting layer 22″ as the trench floors 42″.

In an embodiment in which the material layer 12″ is composed of a material such as silicon oxide (SiO_(x)), the spacer intervals 12 a″ can be removed, for example by a fluoride ion wet etch. In an embodiment in which the material layer 12″ is composed of a negative resist such as a methacrylate-based photoresist, the spacer intervals 12 a″ between trenches 14 a-14 c″ can be selectively developed and then removed by wet processing by applying an appropriate solvent to form new trenches 15 a″-15 b″.

As shown, the spacer material 12 a″ has been removed to define the trench ends or edges 38 a″, 38 b″, and to expose the matrix 32″ (e.g., of PS) of the first self-assembled block copolymer film 28″ to define the sidewalls 40″ of trenches 15 a″-15 b″, which are preferential wetting. The removal of the spacer material 12 a″ is conducted so as not to damage or disrupt the integrity of the first self-assembled block copolymer structure 28″. A residual amount of the spacer material 12 a″ (e.g. of gold) may remain (not shown) on the surface of the matrix 32″ (i.e., sidewalls 40″). The trench edges 38 a″, 38 b″ are aligned with the edges 20 a″, 20 b″ of trenches 14 a″-14 c″. As such, the length (l) of the trenches 14″, 15″ is nL_(o).

Next, as illustrated in FIGS. 9A and 9B, a second SA block copolymer material is deposited (e.g., by spin casting) as a film 46″ into the newly formed trenches 15 a ₁₋₂″-15 b ₁₋₂″. The second block copolymer material 46″ has a period of L_(o) and is neutral wetting to the trench floors 42″, and the major block (e.g., PS) of the second copolymer material is preferential wetting to the sidewalls 40″ and trench edges 38″, 38 b″. The second copolymer material 46″ can be the same or a different composition than the first copolymer material 24″. The thickness (t) of the cast copolymer film 46″ is less than or about equal to the L_(o) value of the second block copolymer material.

The first self-assembled major block (matrix 32″, optionally with a residual amount of spacer 12 a″ (e.g., gold) thereon) that forms the sidewalls 40″ of trenches 15 a″-15 b″, provides a template or boundary condition in the x-axis (

) for the registration of the self-assembling second copolymer film 46″. In addition, the edges 38 a″, 38 b″ provide boundary conditions in the y-axis (

). The trench floors 42″ are neutral wetting, and the matrix 32″ of the first assembled film is preferential wetting to the major block of the second copolymer, allowing graphoepitaxy and the formation of perpendicularly-oriented cylindrical domains within the trenches 15 a″-15 b″. Optionally, ellipticity can be induced in the structures by creating a slight mismatch between the trench width and the inherent pitch (L_(o)) of the block copolymer or ternary blend, as previously described.

The second copolymer film 46″ is then annealed to form the self-assembled block copolymer structure 48″ depicted in FIGS. 10A and 10B. The earlier performed crosslinking step contributes to the structural integrity of the first self-assembled film 28″ during the casting and annealing of the second block copolymer film. The annealed copolymer film comprises a square array of perpendicularly oriented cylindrical domains of a first block of the copolymer within a matrix of a second block, the cylindrical domains in one dimension in a single row at a pitch distance of about L_(o) and aligned with cylindrical domains in a second dimension at a pitch distance of about L_(o).

Upon annealing, the second block copolymer film self-assembles into 1-D arrays of perpendicularly-oriented (PMMA) cylindrical domains 50″ (e.g., of PMMA) within a polymer matrix 52″ (e.g., of PS), which are registered to the sidewalls 40″ (matrix 32″) of the trenches 15 a ₁₋₂″-15 b ₁₋₂″, with the major polymer block (matrix 52″, e.g., of PS) wetting the sidewalls 40″. Each cylinder 50″ is spaced apart within each trench 15 a″-15 b″) by a pitch distance (p_(c)″) of L_(o). The cylinders 50″ are also registered to and aligned with the cylinders 30″ within trenches 14 a-14 c″.

The alignment of the trench edges 38 a″, 38 b″ with edges 20 a″, 20 b″ of the first set of trenches 14 a″-14 c″ in combination with a trench width (w) and trench pitch (p_(t)) between adjacent trenches (e.g., 14 a 3″, 15 a 3″, 14 b 3″, etc.) of about L_(o) produces a self-assembled film 48″ containing two-dimensional (2-D) square arrays 48 a″-48 c″ of cylinders 30″, 50″, with each cylinder within an array being separated by a pitch distance (p_(c)) of L_(o).

Referring now to FIGS. 11A-11C, selective removal of one of the polymer domains (i.e., matrix or cylinders) can then be performed to produce a template for use in patterning the substrate 10″. For example, selective removal of the cylindrical domains 30″, 50″ (e.g., of PMMA) will produce 2-D square arrays of openings 54″ contained within a polymer matrix 32″, 52″ (e.g., of PS), as in FIGS. 11A and 11B. Selective removal of the matrix phase 32″, 52″ of the film will provide 2-D square arrays of cylinders 30″, 50″ and openings 54″, as shown in FIG. 11C. The resulting film can be then used in patterning (arrows ↓↓) substrate 10″ to form openings 35″ in substrate 10″ (shown in phantom). Processing can then be continued as desired.

Another method according to an embodiment of the invention, illustrated with reference to FIGS. 12-18, utilizes both graphoepitaxy (topographic features) and chemical pattern transfer techniques to form a film composed of 2-D rectangular arrays of parallel- and perpendicular-oriented cylinders in a polymer matrix. Graphoepitaxy is used to form arrays in one dimension, and a chemical pattern transfer technique is used to control formation of the arrays in a second dimension.

In the present embodiment, chemical pattern transfer is applied to differentiate and create patterns of wetting preferences in discrete areas on the floors of adjacently positioned trenches as a series of stripes oriented perpendicular to the trench sidewalls. The differing wetting patterns impose ordering on block copolymer films that are then cast on top of the substrate and annealed.

As shown in FIGS. 12A and 12B, in a first step of preparing a patterned or chemically activated surface on the trench floor (18″), a neutral wetting random copolymer brush 22′ (e.g., a random PS-r-PMMA polymer) is coated onto a substrate 10′″, which can be an inherently preferential wetting material such as silicon (with native oxide), oxide (e.g., silicon oxide, SiO_(x)), or inorganic film. The brush layer 22″ is coated with a layer of photoresist 56′″, which is patterned as shown, by optical lithography or other suitable method. The polymer brush layer 22′″ is then etched using the patterned resist layer 56′″ as a mask to expose the underlying preferential wetting substrate 10′″, and the resist layer 56′″ is removed.

In another embodiment, layer 22′″ is composed of a photo-crosslinkable neutral wetting polymer as described, for example, in U.S. Pat. Nos. 6,890,703 and 6,992,115 (Hawker et al.), which can be photoexposed and selectively crosslinked in the desired regions 60′″ by exposure to light through a reticle. In another embodiment, selective crosslinking of the neutral wetting layer 22′″ in defined sections 60′″ can be performed with the use of a patterned photoresist mask. The non-crosslinked regions can then be removed by wet processing using an appropriate solvent.

The resulting structure, depicted in FIGS. 13A and 13B, is patterned with discrete sections 58′″ of the exposed preferential wetting substrate 10′″ (e.g., silicon with native oxide) adjacent to discrete sections 60′″ of the neutral wetting polymer layer 22′″. In some embodiments, the floor pattern is a series of stripes, the neutral wetting stripes or sections 60′″ with a width (w_(r)) at or about nL_(o) and the preferential wetting stripes or sections 58′″ with a width (w_(r)) at or about L_(o). In another embodiment, each of the sections 58′″, 60′″ has a width (w_(r)) at or about L_(o).

A material layer 12′″ (e.g., of SiO_(x)) is then deposited over the substrate as illustrated in FIG. 14, and patterned with a series of trenches to expose the patterned substrate 10′″ as the floor of the trenches, as shown in FIGS. 15A and 15B. In another embodiment, the material layer 12′″ can be deposited on the substrate 10′″, the trenches etched into the material layer to expose the substrate, and the neutral polymer layer 22′″ deposited onto the floors of the trenches, masked and then etched to expose sections 58′″ of the substrate 10′″ within the trenches.

As illustrated in FIG. 15A, the structure has been patterned with three sets of adjacent trenches 14 a ₁₋₃′″-14 c ₁₋₃′″ of width (w) at or about L_(o) and a length (l) of about nL_(o). The widths (w_(s)) of the spacer interval 12 a′″ of the material layer 12′″ between adjacent trenches (e.g., between 14 a ₃′″, 14 b ₃′″, 14 c ₃′″, etc.) is constant and at least L_(o), being L_(o) in the present example. Thus, the pitch distance (p_(t)) of adjacent trenches is about 2*L_(o).

The trench sidewalls 16′″ and edges 20 a′″, 20 b′″ (e.g., of SiO_(x)) are preferential wetting to one block (e.g., PMMA) of the copolymer. The trench floors 18′″ are defined by the alternating preferential wetting sections 58′″ (substrate 10′″) and neutral wetting sections 60′″ (e.g., random copolymer brush 22′″).

Referring now to FIGS. 16A and 16B, with the trench floors chemically patterned, a block copolymer 24′″ with cylindrical morphology of pitch L_(o) or a ternary blend of a block copolymer and homopolymers formulated to have pitch L_(o) can then be cast into the trenches to a film thickness (t) of about L_(o) and annealed. As depicted in FIGS. 17A and 17B, the block copolymer film will then self-assemble in each trench into a 1-D array of a perpendicular-oriented cylindrical domain 62′″ (or a string of such perpendicular domains) extending the width (w_(r)) of each neutral wetting polymer section 60′″ situated between a parallel-oriented cylindrical domain 64′″ (half-cylinder) (or string of such parallel domains) extending the width (w_(r)) of each preferential wetting section 58′.

The annealed copolymer film comprises a rectangular array of cylindrical domains of a first block of the copolymer within a matrix of a second block, the cylindrical domains in one dimension comprising a series of n perpendicular-oriented cylindrical domains 62′″ between two parallel-oriented cylindrical domains 64″ in a single row at a pitch distance of about L_(o), with the cylindrical domains aligned with cylindrical domains in a second dimension at a pitch distance of about 2*L_(o). The annealed copolymer film can be contained within adjacently spaced apart trenches of length m*(n+1)*L_(o) with the ends (edges) 20 a′″, 20 b′″ of the trenches being aligned, and with the cylindrical domains within each trench in a single array and at a pitch distance of about L_(o) and aligned with the cylindrical domains in adjacent trenches at a pitch distance of about 2*L_(o), such that the single array within each trench comprises a perpendicular oriented cylinder 62′″ or n cylinders between two parallel-oriented cylinders 64′″.

The edge 66′″ between the sections 58′″, 60′″ provides a boundary condition for the sharp transition between parallel- and perpendicular-oriented cylinders and imposes order in one-dimension (1-D) within each trench. The resulting structure is an ordered 1-D array of alternating perpendicular- and parallel-oriented cylinders for the length (nL₀) of each trench. Alternatively, the structure is a repeating series of n perpendicular cylinders separated by a region of parallel cylinder morphology, e.g., the trench length is m*(n+1)*L_(o), where m is the number of preferential-wetting chemically patterned stripes and n is the number of features or structures (e.g., where m and n are independently 1-50).

The inversion from perpendicular to parallel cylinders that occurs at the boundary edges 66′″ imposes a second dimensional constraint whereby the structures in adjacent trenches (rows) are also aligned in a second dimension. The resulting structure is a 2-D rectangular array of sublithographic cylindrical structures in alternating perpendicular and parallel orientations.

Referring now to FIGS. 18A and 18B, selective removal of one of the polymer domains (i.e., matrix or cylinders) can then be performed to produce a template for use in patterning the substrate 10′″. For example, selective removal of the cylindrical domains 62′″, 64′″ (e.g., of PMMA) will produce 2-D rectangular arrays of openings 68′″, 70′″ contained within a polymer matrix 72′″ (e.g., of PS). The resulting film can be then used in patterning substrate 10′″. The configuration of the openings will vary according to the orientation of the cylindrical domains within the trenches. Only openings 68′″ will extend to the trench floor 18′″, thus the structure forms an etch mask which can selectively transfer the structural pattern of the perpendicular cylinders 62′″ to the underlying substrate (shown as phantom openings 74′″).

Embodiments of the invention provide ordering of domains over a large area, and control the location and orientation of ordered cylindrical domains in two dimensions. Such features can be prepared more inexpensively than by electron beam lithography or EUV photolithography. The feature sizes produced and accessible by this invention cannot be prepared by conventional photolithography.

EXAMPLE I

Trenches 250 nm deep with widths ranging from 75 nm to 600 nm having silicon oxide sidewalls and silicon oxycarbide floors were provided. On several of the wafers, oxide was deposited onto the sidewalls and the trench floors. Both types of trench floors were treated to be neutral wetting to PS and PMMA.

To get perpendicular cylinders, a random PS:PMMA copolymer solution (about 58% PS) containing a crosslinking agent was cast as a film of about 5-10 nm thick onto the features, and annealed at about 160° C. for 4 hours. Capillary forces pulled the PS-r-PMMA to the trench floor prior to complete crosslinking, leaving oxide sidewalls that were preferential-wetting to PMMA. The resulting trench structure had sidewalls that were preferential wetting with the random copolymer layer as a mat on the bottom of the trenches, which provided a neutral wetting surface.

A 0.425% solution of cylinder-forming PS-b-PMMA in toluene was then cast onto the treated substrates so as to form a film about 30-40 nm thick. The PS-b-PMMA material (46K/21K PS:PMMA; 67K MW) was formulated to foam PMMA-phase cylinders (diameter ˜20 nm) at repeat periods (pitch) of about 35 nm in the middle of a PS matrix. However, the arrays in adjoining trenches were not aligned.

In about 75 nm wide trenches, two rows of cylinders were formed that were slightly offset from each other, forming a “zigzag” structure in a regular registered pattern with each side being equidistant from the sidewall of the trench.

EXAMPLE 2

Ternary blends (10-40%) of homopolymers (20 K PS, 20 K PMMA) were prepared in 0.425% solutions of 46K/21K PS-b-PMMA in toluene. These solutions were cast onto the substrates described above at thicknesses of 30-40 nm. The addition of homopolymers swells the domain sizes of the two fractions, resulting in an increased inherent pitch value (L_(o)) of the polymer.

At 10-20% homopolymers, a two row zigzag pattern of cylinders was formed as seen by SEM. With 30% homopolymers content, the zigzag pattern began to break down and numerous errors and unusual morphologies were observed. When a ternary blend of 46/21 PS-b-PMMA block copolymer with 40% 20 PS and 20K PMMA homopolymers was cast and annealed onto the same substrate (i.e., 80 nm wide trenches, (P(S-r-BCB-r-MMA)) floor, oxide sidewalls), single rows of perpendicular cylinders with apparent diameter of about 35 nm formed in the 80 nm wide trenches. At 40% homopolymers, the mixture caused a pitch of about 50 nm, resulting in the formation of a one-dimensional (1-D) array (single row) of cylinders. This is an example of graphoepitaxy technique in which lithographically defined physical features are used to cause ordering of block copolymer films. The cylinder arrays in adjacent trenches were not aligned and were off-set along the y-axis.

The results show that the boundary condition of the preferential wetting sidewalls and neutral wetting floor within a trench of width equal to the inherent pitch value (L_(o)) of the self-assembling polymer film enforced the formation of a single row of cylinders. The results also demonstrate that, by increasing L_(o) so that it is a closer match to the sidewalls, there is a shift from a two row structure to a one row structure.

Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement which is calculated to achieve the same purpose may be substituted for the specific embodiments shown. This application is intended to cover any adaptations or variations that operate according to the principles of the invention as described. Therefore, it is intended that this invention be limited only by the claims and the equivalents thereof. The disclosures of patents, references and publications cited in the application are incorporated by reference herein. 

What is claimed is:
 1. A method of fabricating a polymeric material, the method comprising: masking a neutral wetting material situated on a preferential wetting substrate to form masked and unmasked sections, each unmasked section having a width of about L_(o), and each masked section having a width of about nL_(o); removing the unmasked sections of the neutral wetting material to expose the preferential wetting substrate; removing the mask to expose the sections of the neutral wetting material; forming an overlying material over the sections of the preferential wetting substrate and the neutral wetting material; forming a plurality of trenches in the overlying material to expose the sections of the preferential wetting substrate and the neutral wetting material oriented perpendicular to sidewalls of the trenches, each trench having preferential wetting sidewalls and ends, a width of about L_(o), a length of about m*(n+1)−*L_(o), where m is a number of sections of the preferential wetting substrate, n is a number of perpendicularly oriented cylinders, and m and n are independently 1-50, the ends of the trenches being aligned, and a pitch distance between adjacent trenches of at least about 2*L_(o); forming a block copolymer material within the trenches; and causing the block copolymer material to self-assemble into cylinders of a first polymer block of the block copolymer material in a matrix of a second polymer block within each trench, the cylinders situated on the sections of the neutral wetting material in a perpendicular orientation to the preferential wetting substrate, and the cylinders situated on the sections of the preferential wetting substrate in a parallel orientation to the preferential wetting substrate, each trench containing m rows of n cylinders with the cylinders within each trench at a pitch distance of about L_(o) and the cylinders between adjacent trenches at a pitch distance of about 2*L_(o).
 2. The method of claim 1, wherein the block copolymer material comprises from about 60:40 to about 80:20 ratio of the first polymer block to the second polymer block.
 3. The method of claim 1, wherein the block copolymer material comprises a blend of the block copolymer material and a homopolymer of the first polymer block, the second polymer block, or both.
 4. The method of claim 1, wherein the block copolymer material within the trenches has a thickness of about L_(o).
 5. The method of claim 1, further comprising forming the neutral wetting material on the preferential wetting substrate.
 6. The method of claim 1, wherein the neutral wetting material comprises a random copolymer.
 7. The method of claim 1, wherein the neutral wetting material comprises hydrogen-terminated silicon.
 8. The method of claim 1, wherein the preferential wetting substrate comprises silicon.
 9. The method of claim 1, further comprising applying a preferential wetting material to the ends and sidewalls of the trenches.
 10. The method of claim 1, wherein the sidewalls and ends of the trenches comprise a preferential wetting material selected from the group consisting of silicon oxide, silicon nitride, silicon oxycarbide, metal, and resist material.
 11. The method of claim 1, wherein the block copolymer material on the sections of the neutral wetting material self-assembles into a single row of perpendicularly oriented cylinders.
 12. The method of claim 1, wherein causing the block copolymer material to self-assemble comprises thermally annealing the block copolymer material.
 13. The method of claim 1, wherein causing the block copolymer material to self-assemble comprises solvent annealing the block copolymer material.
 14. The method of claim 1, further comprising, after causing the block copolymer material to self-assemble, selectively removing the first polymer block to provide openings within the matrix of the second polymer block.
 15. The method of claim 14, further comprising, prior to selectively removing the first polymer block, crosslinking the self-assembled block copolymer.
 16. The method of claim 14, further comprising etching the preferential wetting substrate through the openings.
 17. A method of fabricating a polymeric material, the method comprising: forming a plurality of trenches in a material overlying a substrate, each trench having a preferential wetting floor, sidewalls and ends, a width of about L_(o) and a length, the ends of the trenches being aligned, a pitch distance between adjacent trenches being at least about 2*L_(o); forming a neutral wetting material onto the preferential wetting floor of the trench; masking the neutral wetting material to form masked and unmasked sections oriented perpendicular to sidewalls of the trenches, each unmasked section having a width of about L_(o), each masked section having a width of about nL_(o); removing the unmasked sections of the neutral wetting material to expose sections of the preferential wetting floor of the trench; removing the mask to expose sections of the neutral wetting material; forming a block copolymer material within the trenches; and causing the block copolymer material to self-assemble into cylinders in a polymer matrix within each trench, the cylinders situated on the sections of the neutral wetting material in a perpendicular orientation to the substrate, cylinders situated on the sections of the preferential wetting floor of the trench in a parallel orientation to the substrate, each trench containing m rows of n cylinders with the cylinders within each trench at a pitch distance of about L_(o) and the cylinders between adjacent trenches at a pitch distance of about 2*L_(o).
 18. The method of claim 17, wherein the length of the trenches is about m*(n+1)−*L_(o), where m is a number of sections of the preferential wetting floor of the trenches, n is a number of perpendicularly oriented cylinders, and m and n are independently 1 to
 50. 19. A polymeric material situated within adjacently spaced apart trenches, ends of the trenches being aligned, the polymeric material comprising a rectangular array of perpendicularly oriented cylindrical domains of a first block of a block copolymer within a matrix of a second block of the block copolymer, the perpendicularly oriented cylindrical domains within each trench in a single array at a pitch distance of about L_(o) and aligned with the cylindrical domains in adjacent trenches at a pitch distance of about 2*L_(o).
 20. A polymeric material comprising a rectangular array of perpendicularly oriented cylindrical domains of a first block of a block copolymer within a matrix of a second block of the block copolymer, the perpendicularly oriented cylindrical domains in one dimension at a pitch distance of about L_(o) and aligned with perpendicularly oriented cylindrical domains in a second dimension at a pitch distance of about 2*L_(o).
 21. A polymeric material comprising a square array of perpendicularly oriented cylindrical domains of a first block of a block copolymer within a matrix of a second block of the block copolymer, the perpendicularly oriented cylindrical domains in a single array at a pitch distance of about L_(o) and aligned with adjacent perpendicularly oriented cylindrical domains at a pitch distance of about L_(o).
 22. A polymeric material comprising a square array of perpendicularly oriented cylindrical domains of a first block of a block copolymer within a matrix of a second block of the block copolymer, the perpendicularly oriented cylindrical domains in a first dimension in a single row at a pitch distance of about L_(o) and aligned with perpendicularly oriented cylindrical domains in a second dimension at a pitch distance of about L_(o).
 23. A polymeric material comprising an annealed block copolymer material within adjacently spaced apart trenches, ends of the trenches being aligned, the annealed block copolymer material comprising a rectangular array of cylindrical domains of a first block of the block copolymer material within a matrix of a second block of the block copolymer material, the cylindrical domains within each trench in a single array at a pitch distance of about L_(o) and aligned with the cylindrical domains in adjacent trenches at a pitch distance of about 2*L_(o), wherein the single array within each trench comprises n perpendicularly oriented cylinders between two parallel-oriented cylinders.
 24. A polymeric material comprising a rectangular array of cylindrical domains of a first block of a block copolymer within a matrix of a second block of the block copolymer, the cylindrical domains in a first dimension comprising n perpendicularly oriented cylinders between two parallel-oriented cylinders in a single row at a pitch distance of about L_(o), the cylindrical domains in the first dimension aligned with cylindrical domains in a second dimension at a pitch distance of about 2*L_(o). 